{"id":160,"date":"2019-06-26T22:49:07","date_gmt":"2019-06-26T22:49:07","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=160"},"modified":"2019-12-09T22:41:18","modified_gmt":"2019-12-09T22:41:18","slug":"pascals-triangle-2","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/pascals-triangle-2\/","title":{"rendered":"Pascal’s Triangle"},"content":{"rendered":"\n
\"\"<\/figure><\/div>\n\n\n\n

Consider the triangle in Figure 1, called Pascal’s triangle<\/em>. It consists of numbers where each entry is the sum of the two entries above it.<\/p>\n\n\n\n

Do you recognize the numbers in each row? This a quick way to generate the coefficients of (x+y)n<\/sup> from algebra!<\/p>\n\n\n\n

And, better yet, you can use them as a quick way to calculate the powers of 11, since 11=10+1. Notice that 11, 121, 1331, and 14641 are all powers of 11…<\/p>\n\n\n\n

Presentation Suggestions:<\/strong>
Draw several rows. Ask what 114<\/sup> and 115<\/sup> are! As a challenge, 116<\/sup> is harder; you have to carry…<\/p>\n\n\n\n

The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong>
The generation of Pascal’s triangle works because in long multiplication of a polynomial by (x+y), you end up adding adjacent coefficients of the\u00a0polynomial\u00a0together. The Fun Fact\u00a0Multiplication By 11\u00a0is based on this idea.<\/p>\n\n\n\n

How to Cite this Page:<\/strong> 
Su, Francis E., et al. “Pascal’s Triangle.” Math Fun Facts<\/em>. <http:\/\/www.math.hmc.edu\/funfacts>.<\/p>\n\n\n\n

Fun Fact suggested by:   <\/strong>
Francis Su <\/p>\n","protected":false},"excerpt":{"rendered":"

Consider the triangle in Figure 1, called Pascal’s triangle. It consists of numbers where each entry is the sum of the...<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[2,13,9,3,10,15],"class_list":["post-160","page","type-page","status-publish","hentry","tag-algebra","tag-binomialcoefficients","tag-combinatorics","tag-easy","tag-numtheory","tag-polynomial"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/160","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/comments?post=160"}],"version-history":[{"count":3,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/160\/revisions"}],"predecessor-version":[{"id":1559,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/160\/revisions\/1559"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=160"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}